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A pentagonal rotunda adjoined to a decagonal prism which is Johnson solid J_(21).

An n-gonal pyramid adjoined to an n-gonal prism.

Johnson solid J_(19).

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

The evolute of the epicycloid x = (a+b)cost-bcos[((a+b)/b)t] (1) y = (a+b)sint-bsin[((a+b)/b)t] (2) is another epicycloid given by x = a/(a+2b){(a+b)cost+bcos[((a+b)/b)t]} ...

The involute of the epicycloid x = (a+b)cost-bcos[((a+b)/b)t] (1) y = (a+b)sint-bsin[((a+b)/b)t] (2) is another epicycloid given by x = (a+2b)/a{(a+b)cost+bcos[((a+b)/b)t]} ...

The radial curve of an epicycloid is shown above for an epicycloid with four cusps. Although it is claimed to be a rose curve by Lawrence (1972), it is not.

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...

The inverse curve of the epispiral r=asec(ntheta) with inversion center at the origin and inversion radius k is the rose curve r=(kcos(ntheta))/a.

The parametric equations of the evolute of an epitrochoid specified by circle radii a and b with offset h are x = ...